Showing papers in "Progress of Theoretical Physics in 1989"

Temporal Intermittency in the Energy Cascade Process and Local Lyapunov Analysis in Fully-Developed Model Turbulence

Abstract: Le processus de cascade d'energie est etudie numeriquement sur un modele scalaire de la turbulence tridimensionnelle entierement developpee. L'energie se propage a travers l'intervalle inerte par intermittence, comme des explosions alternant avec des periodes de repos (on revoit le point de vue de Siggia). Pendant la phase activee, le premier exposant de Lyapunov local oscille fortement et le support du premier vecteur de Lyapunov s'etend sur le sous-intervalle inerte

Mastersymmetries and Multi-Hamiltonian Formulations for Some Integrable Lattice Systems

Abstract: On obtient des quantites conservees, une formulation bi-hamiltonienne, une structure recursive et des symetries hereditaires pour un nombre de systemes reticulaires ayant une signification physique. On donne, pour les solutions multisolitons, des variables d'angle. A part le reseau de Toda bien etudie, ces systemes incluent: un reseau de Volterra, un systeme Network concentre, un reseau de Kac-Moerbeke-Langmuir et une classe d'equations de Network. On n'utilise pas la representation de Lax ou toute autre information additionnelle concernant les equations etudiees. Toutes les quantites sont trouvees d'une maniere purement algorithmique en utilisant les symetries maitresses

Stochastic Dynamics of an Inflationary Model and Initial Distribution· of Universes

Abstract: We investigate the stationary solution of the modified Fokker· Planck equation which governs the global dynamics of the inflation. Contrary to the original FP equation which is for a: Hubble horizon size region, we found that the normalizable stationary solution can exist for modified Fokker-Planck equation which is for many Hubble horizon size regions. For a chaotic inflationary model with the potential Aq:>2n, we get initial distribution of classical universes using this solution, and discussed the physical meaning of it. Especially for n=2, this distribution obeys power-law and classical universes which, created from the Planck energy region, make the fractal structure. In other cases n=l=2, creation of large classical universes is strongly suppressed. § 1. Introduction An inflationary model was proposed to solve many problems in the standard cosmological model. In this model, background geometry experiences exponentially expanding de Sitter stage. By this exponential expansion, problems contained in the standard cosmological model can be solved. Furthermore, a natural explanation for the origin of the density fluctuations is obtained by considering quantum fluctuations of the scalar field in de Sitter expanding space-time. When one considers dynamics of an inflationary model, quantum aspect of a scalar field becomes very important. In a classical picture, dynamics of the model is as follows: At some time, potential energy of the scalar field dominates the energy momentum tensor, and this becomes . an effective cosmological constant. Then background space-time begins to expand exponentially. At this time, owing to a large friction force arising from exponential expansion, the acceleration of the scalar field becomes negligible compared to the velocity and the slow rolling condition is attained. The value of the scalar field rolls down a hill of potential very slowly. Due to this slow rolling, we can get sufficient duration of de Sitter expansion to solve problems in standard cosmology. But this picture must be changed when inflation is treated with quantum theory and we must be careful about difference, what variable can be treated as classical. But it is very difficult to solve full quantum field theory and get dynamics from it. Recently stochastic treatment of an inflationary model is studied by many people. 1H3 ) This method describes dynamics of a long wave mode of the scalar field which drives de Sitter expansion. Starting from the operator Heisenberg equation of the scalar field on de Sitter space-time, one, gets a "classical" Langevin equation by coarse graining the short' wave length modes of the scalar field. In this equation, quantum effect enters 'as a Gaussian white noise and dynamics of the long wave mode of the scalar field becomes a stochastic process driven by this noise. In spite of treating a quantum system, the only thing one has to do is to solve a c-number stochastic equation. Therefore it becomes fairly easy to understand the dynamics of

Quantum Mechanics in Riemann Manifold

Abstract: The quantum mechanics on the hypersurface VN-1 embedded in Euclidean space RN is examined. The quantization is done in accordance with Dirac method, and as a result some additional term proportional to ħ^2 appears in the potential energy. This term has the information of exterior to the hypersurface; thus, the quantum mechanics in Riemann space without any kind of exterior world is different from quantum mechanics on hypersurface embedded in Euclidean space.

Abelian Confinement Mechanism in QCD

Abstract: It is shown explicitly that quarks and gluons, dynamical as well as static, are confined in QCD if color magnetic monopoles in the abelian gauge condense. The mass generation essential fbr the confinement occurs from the spontaneous breaking of color magnetic Um(l) symmetry, whereas color electric Ue(l) remains unbroken.

Thermal Bethe-Ansatz Method for the Spin-1/2 XXZ Heisenberg Chain

Abstract: A new method is proposed for calculating the free energy of the one·dimensional spin·l/2 XXZ Heisenberg model. The partition function is written in terms of the transfer matrix for a two· dimensional Ising system, whose maximum eigenvalue is obtained by the Bethe·ansatz method leading to the free energy in the thermodynamic limit. This method uses no such assumption as the completeness of the Bethe states that has been proved only partially and yields better results than the previous methods do.

Numerical Simulations of Interaction between Stellar Wind and Interstellar Medium

Abstract: Hydrodynamic interaction between supersonic spherical wind emitted from an astronomical object and a uniform streaming flow is simulated numerically assuming the flow to be axisymmetric, adiabatic and inviscid. Examples of such a phenomenon are a comet in the solar wind, and the solar wind or a stellar wind in an interstellar medium. Three cases of the incident flow, i.e., subsonic, supersonic and hypersonic flow, are considered. Discontinuities in the flow, i.e., a bow shock, a contact surface, an inner shock, a Mach disc and a slip surface are identified. The contact surface and the slip surface are found to be Kelvin- Helmholtz unstable. Other instabilities occurring near the stagnation region and the inner shock are also found.

Gauge Groups of ZN Orbifold Models

Abstract: Z_N orbifold models which have N=1 space-time supersymmetry are cxamined. All gauge groups of Z_N orbifold models are classified completely.

Chiral Symmetry Breaking and Nonperturbative Scale Anomaly in Gauge Field Theories

Abstract: The nonperturbative dynamics of chiral and scale symmetry breaking in asymptotically free and non-asymptotically free (with an ultraviolet stable fixed point) vector-like gauge theories is inves­ tigated. In the two-loop approximation analytical expressions for the chiral and gluon condensates are obtained. The hypothesis about a soft behaviour at small distances of composite operators in non-asymptotically free gauge theories with a fixed point is put forward and substantiated. It is shown that in these theories the form of the scale anomaly depends on the type of the phase in coupling constant to which it relates. The two component conception of scale symmetry breaking in gauge theories is suggested. The mass relation for the singlet scalar fermion-antifermion bound state is obtained. The important ingredient of this approach is a large (d""'2) dynamical dimension of composite chiral fields. The application of this approach to QeD and technicolour models is discussed.

Scaling Structures and Statistical Mechanics of Type I Intermittent Chaos

Abstract: Le chaos intermittent presente des mouvements laminaires reguliers et des explosions turbulentes irregulieres alternativement, indiquant que son attracteur chaotique possede deux types differents de structures locales. Pour l'intermittence de type I juste avant la bifurcation de nœud-selle, les deux types de structures locales peuvent etre captures par le spectre de fluctuation λ(Λ) des vitesses de developpement locales semi-fixes Λ des orbites toutes proches et leur moyenne q-ponderee Λ(q), (−∞

Intrinsic Fluctuation and Its Critical Scaling in a Class of Populations of Oscillators with Distributed Frequencies

Abstract: Large populations of coupled dissipative oscillators exhibit macroscopic mutual entrainment when coupling is strong enough to compensate for the disordering effect due to the distribution of natural frequencies of oscillators. This phenomenon has much relevance to a variety of fields in science (e.g., see Ref. 1», and quite a few investigations have been devoted to elucidating it. Of these, studies with emphasis on the aspect of a ph,ase transition may be particularly interesting and important since they open a new area in the field of critical phenomena to clarify how the onset of mutual entrainment in oscillator assemblies compares to conventional phase transi­ tions in diverse equilibrium systems. 2 ) In this paper we attempt a study along such a line using the following model :3)

Neutron Diffusion and Nucleosynthesis in the Inhomogeneous Universe

Abstract: On etudie la nucleosynthese dans l'univers avec des fluctuations de densite isothermes. Les neutrons, dans les regions de faible densite diffusent en retour vers des regions de densite elevee. Les abondances des elements legers sont donc contradictoires avec Ω B =1 si l'echelle des fluctuations de densite est aussi petite que 10 4 cm a T=1 MeV

Fermi Liquid Theory on the Basis of the Periodic Anderson Model with Spin-Orbit Coupling and Crystalline Field

Abstract: In order to discuSs the normal-state properties of heavy-fermion systems, the Fermi liquid theory is developed on the basis of the periodic Anderson model with arbitrary spin-orbit coupling and crystalline field. For the unperturbed (U =0) case, the electronic band structure is determined; then the expressions of T-linear coefficif:mt of specific heat and magnetic susceptibility are derived. For U =1= 0, the general expressions for T -lineGlr coefficient of specific heat and magnetization are derived. However, the expression for magnetic susceptibility cannot generally be brought into such a usual form that includes only the quantities on the Fermi surface because of the existence of off-diagonal elements of I-electron self-energy. Therefore, the susceptibility is calculated in the special case that only the lowest Kramers doublet is taken into account.

q-Phase Transitions in Chaotic Attractors of Differential Equations at Bifurcation Points

Abstract: Most nonlinear ordinary differential equations exhibit chaotic attractors which have singular local structures at their bifurcation points. By taking the driven damped pendulum and the Duffing equation, such chaotic attractors are studied in terms of the q-phase transitions of a q-weighted average A(q), (-oo

Derivation of Gauge and Gravitational Induced Chern-Simons Terms in Three Dimensions

Abstract: On etudie la theorie des fermions couples a une jauge externe et a des champs gravitationnels. A trois dimensions, l'existence de fermions massifs conduit au terme de Chern-Simons induit. On obtient le terme de Chern-Simons induit par une methode d'integrale de parcours

Numerical study of vortex motion in the two dimensional Ginzburg-Landau equation

Abstract: The spiral pattern can emerge in the two dimensional generalized Ginzburg·Landau equation. There exists a vortex as a topological defect in the center of the spiral. We carried out some numerical simulations to study the motion of an interacting pair of vortices and a vortex driven by the faster pacemaker. . 7 Spiral patterns and targetlikepatterns are interesting and well-known wave patterns in the Belousov-Zhabotinsky reaction. 1 ),2) Such waves can emerge generally in two dimensional excitable or oscillatory media. 1l - 7 ) We consider only oscillatory media in the following. There is a pacemaker region in the center of such patterns and it sends out the waves. For the targetlike pattern the pacemaker arises from heterogeneous nuclei in the vicinity of which the oscillation frequency is somewhat higher than that of bulk medium. For the spiral pattern there is a singularity point in the center of the spiral, where the amplitude of oscillation becomes zero and the phase of oscillation cannot be defined. The phase singularity point is a kind of topological defects called vortex and it plays a role of the pacemaker. A three dimensional extension of rotating spiral waves is called scroll waves and there is a vortex line in the center of the scrol1. 3 ),4) It is known experimentally that many spiral patterns coexist stably and they move around hardly. It is also known that if spiral patterns and targetlike patterns coexist initially, the targetlike patterns are gradually eaten away by the spiral patterns and eventually all the targetlike patterns disappear and only the spiral patterns survive. It is because the pace of oscillation of the spiral wave is generally faster than that of targetlike waves. We carried out numerical simulations to see if the spiral patterns are really stable and cannot move. The model equation we used in this paper is the generalized